It's a very complex issue. It's not just about having social engagement, but also what type of social engagement and with who.
I'm pretty certain that for the elderly, no company is better than "lousy" company.
Living alone does not mean that a senior is less socially engaged, just as living with a family does not mean a senior is socially engaged.
A senior living alone could have many friends by participating in many activities, whereas the one living with family members may not interact at all with members of the household who are too busy.
It would not be entirely correct to say that every old man and old woman living alone suffers from loneliness. Some are perfectly fine being left alone. As long as they have their own interests, hobbies and things to keep themselves fully occupied, they do not need to talk to other people all the time and their privacy should be respected.
Inform them of the opportunities available for them to meet others. Knowing how to use the Internet can be the first step.
Some of the elderly prefer solitude to multitude.